4 Reconstruction of Retinal OCT Images with Sparse Representation
91
and 4.12b) have more areas exhibiting striped blurring (e.g. blue ellipse areas) than
their regularly sampled counterparts (Figs. 4.11d and 4.12d). Based on this, we tested
the Tikhonov [15], Bicubic, BM3D [40] +Bicubic and the proposed SBSDI method
on regularly sampled images (Fig. 4.11c). For better visual comparison, we mark
and magnify three boundary areas (boxes #2, 3, 4) in these images. Results from the
Tikhonov, Bicubic, and ScSR methods appeared noisy with indistinct boundaries for
many meaningful anatomical structures. Although the BM3D [53] +Bicubic technique delivers improved noise suppression, it introduces splotchy/blocky (cartoonish)
artifacts. By contrast, application of our SBSDI method that exploits the 3D information resulted in noticeably improved noise suppression while preserving details
compared to other methods. Especially in the regions marked by red boxes #3, 4, the
SBSDI result even shows clearer layers compared with the densely sampled averaged
image (Figs. 4.11j and 4.12j).
4.3.3 3D Adaptive Sparse Representation Based Compression
(3D-ASRC)
As described in Sect. 4.2, the traditional compression method is only designed for
the 2-D image. In common clinical scanning protocols, neighboring OCT slices have
very similar content in many regions, as can be observed in Fig. 4.13b. On the other
hand, those same nearby slices can also exhibit localized differences (see the areas
labeled with the red rectangles in Fig. 4.13b). Therefore, the 3D-ASRC algorithm
was proposed for the compression of 3D OCT images, which can utilize the high
correlations while still considering the differences of nearby slices. The proposed 3DASRC method is composed of three main parts: (a) 3D adaptive sparse representation;
(b) 3D adaptive encoding; (c) decoding and reconstruction, which will be described
in the following subsections. The outline of the proposed 3D-ASRC algorithm is
illustrated in Fig. 4.14.
4.3.3.1 3D Adaptive Sparse Representation
The volume of OCT B-scans are divided into several groups, each with T nearby
slices according to the similarities among them [54] and each slice in an OCT volume
is partitioned into many non-overlapping patches with the mean of each patch is
subtracted from them. Meanwhile, we define nearby patches as a set of patches
centered around the patch x
1
i from slices in the same group as
x
t
i
T
t1
, where t
denotes a particular B-scan in that group. The i in
x
t
i
T
t1
indexes the i-th nearby
patch of the similar group. By rewriting Eq. (4.2), the sparse coefficient vectors
α
t
i
T
t1
of the nearby patches
x
t
i
T
t1
can be obtained by optimizing:
91
and 4.12b) have more areas exhibiting striped blurring (e.g. blue ellipse areas) than
their regularly sampled counterparts (Figs. 4.11d and 4.12d). Based on this, we tested
the Tikhonov [15], Bicubic, BM3D [40] +Bicubic and the proposed SBSDI method
on regularly sampled images (Fig. 4.11c). For better visual comparison, we mark
and magnify three boundary areas (boxes #2, 3, 4) in these images. Results from the
Tikhonov, Bicubic, and ScSR methods appeared noisy with indistinct boundaries for
many meaningful anatomical structures. Although the BM3D [53] +Bicubic technique delivers improved noise suppression, it introduces splotchy/blocky (cartoonish)
artifacts. By contrast, application of our SBSDI method that exploits the 3D information resulted in noticeably improved noise suppression while preserving details
compared to other methods. Especially in the regions marked by red boxes #3, 4, the
SBSDI result even shows clearer layers compared with the densely sampled averaged
image (Figs. 4.11j and 4.12j).
4.3.3 3D Adaptive Sparse Representation Based Compression
(3D-ASRC)
As described in Sect. 4.2, the traditional compression method is only designed for
the 2-D image. In common clinical scanning protocols, neighboring OCT slices have
very similar content in many regions, as can be observed in Fig. 4.13b. On the other
hand, those same nearby slices can also exhibit localized differences (see the areas
labeled with the red rectangles in Fig. 4.13b). Therefore, the 3D-ASRC algorithm
was proposed for the compression of 3D OCT images, which can utilize the high
correlations while still considering the differences of nearby slices. The proposed 3DASRC method is composed of three main parts: (a) 3D adaptive sparse representation;
(b) 3D adaptive encoding; (c) decoding and reconstruction, which will be described
in the following subsections. The outline of the proposed 3D-ASRC algorithm is
illustrated in Fig. 4.14.
4.3.3.1 3D Adaptive Sparse Representation
The volume of OCT B-scans are divided into several groups, each with T nearby
slices according to the similarities among them [54] and each slice in an OCT volume
is partitioned into many non-overlapping patches with the mean of each patch is
subtracted from them. Meanwhile, we define nearby patches as a set of patches
centered around the patch x
1
i from slices in the same group as
x
t
i
T
t1
, where t
denotes a particular B-scan in that group. The i in
x
t
i
T
t1
indexes the i-th nearby
patch of the similar group. By rewriting Eq. (4.2), the sparse coefficient vectors
α
t
i
T
t1
of the nearby patches
x
t
i
T
t1
can be obtained by optimizing: